Úprava lomeného výrazu
Uprav v \mathbb{R} lomený výraz a urči podmínky:
\large \Large \frac{u^{2}+v^{2}}{ \left( u+v \right) ^{2}}\large + \Large \frac{\frac{2}{uv}}{ \left( \frac{1}{u}+\frac {1}{v} \right) ^{2}}\large
= \frac {{\frac{{u^{2}\ +\ 2uv\ +\ v^{2}}} {{{{\left( {uv} \right)}^2}}}}} {{\frac{{u^{2}\ +\ 3uv\ +\ v^{2}}}{{{{\left( {uv} \right)}^2}}}}} =
=1
\large u \neq- v,u \neq 0,v \neq 0
= \frac {{\frac{{u^{2}\ +\ 2uv\ +\ v^{2}}} {{{{\left( {uv} \right)}^2}}}}} {{\frac{{u^{2}\ +\ 2uv\ +\ v^{2}}}{{{{\left( {uv} \right)}^2}}}}} =
=1
\large u \neq- v,u \neq 0,v \neq 0
= \frac {{\frac{{u^{2}\ +\ 2uv\ +\ v^{2}}} {{{{\left( {uv} \right)}^2}}}}} {{\frac{{u^{2}\ +\ 2uv\ +\ v^{2}}}{{{{\left( {uv} \right)}^2}}}}} =
=2
\large u \neq- v,u \neq 0,v \neq 0
= \frac {{\frac{{u^{2}\ +\ 2uv\ +\ v^{2}}} {{{{\left( {uv} \right)}^2}}}}} {{\frac{{u^{2}\ +\ 2uv\ +\ v^{2}}}{{{{\left( {uv} \right)}^3}}}}} =
=1
\large u \neq- v,u \neq 0,v \neq 0